Initial state preparation routines and resource estimates

Develop detailed initial state preparation routines for the real-space first-quantized pre-Born–Oppenheimer molecular wavefunction compatible with the presented qubitization algorithm, and provide associated resource estimates.

Background

The paper focuses on building an efficient block-encoding and qubitization-based time evolution for pre-Born–Oppenheimer dynamics on a real-space grid and argues that initial state preparation is expected to have subdominant cost relative to time evolution.

While they briefly note that their initial state preparation aligns with da Jornada et al. (2025) up to a QFT, the authors explicitly leave the detailed construction and resource estimation of initial state routines for future work.